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Near-optimum Universal Graphs for Graphs with Bounded Degrees
[chapter]

2001
*
Lecture Notes in Computer Science
*

Let H(k, n) denote the family of

doi:10.1007/3-540-44666-4_20
fatcat:b34jss2oarahbaiblgkgqbldpm
*graphs*on n vertices*with*maximum*degree*at most k. ...*For*each fixed k and each n sufficiently large, we explicitly construct an H(k, n)-*universal**graph*Γ (k, n)*with*O(n 2−2/k (log n) 1+8/k ) edges. ... Here we construct*near*-*optimum**universal**graphs**for*families of boundeddegree*graphs*. ...##
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Implementation and Comparison of Vertex Cover Problem using Various Techniques

2016
*
International Journal of Computer Applications
*

and found that all the algorithms give

doi:10.5120/ijca2016910453
fatcat:bbq5vvm4ofdsjjie6nb2bzzmye
*near**optimum*solution*with*a negligible performance difference. ... Such problems are solved by algorithms which promise to give*near**optimum*solution. ... So,*for*few bigger*graphs*Alom's principle procedure may not return the accurate*optimum*resolution . ...##
###
Reducing Maximum Stretch in Compact Routing

2008
*
IEEE INFOCOM 2008 - The 27th Conference on Computer Communications
*

This may be a valuable tool

doi:10.1109/infocom.2008.76
dblp:conf/infocom/EnachescuWG08
fatcat:yugru5fjdrdkpif7cfsgo76oku
*for*obtaining*near*-*optimum*stretch-space tradeoffs*for*specific*graphs*. ... Our scheme produces routing tables that use no more than O(log n) more space than the*optimum*scheme*for*achieving stretch s*with*L landmarks. ... This may be a valuable tool*for*obtaining*near*-*optimum*stretchspace tradeoffs*for*specific*graphs*. ...##
###
Reducing Maximum Stretch in Compact Routing

2008
*
2008 Proceedings IEEE INFOCOM - The 27th Conference on Computer Communications
*

This may be a valuable tool

doi:10.1109/infocom.2007.76
fatcat:fe2ywqihwvb35kv2i2cs5635vy
*for*obtaining*near*-*optimum*stretch-space tradeoffs*for*specific*graphs*. ... Our scheme produces routing tables that use no more than O(log n) more space than the*optimum*scheme*for*achieving stretch s*with*L landmarks. ... This may be a valuable tool*for*obtaining*near*-*optimum*stretchspace tradeoffs*for*specific*graphs*. ...##
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Page 25 of IEEE Transactions on Computers Vol. 52, Issue 1
[page]

2003
*
IEEE Transactions on Computers
*

The basic method is, first, to give a lower

*bound*fo e(k VM*with*the number of edges equal to the lower*bound*2.V and, then, to find a hyper-*universal*k-partite*graph*Theorem 4. « W and the*graph*is an ... But, here, we use different methods as this will help us in the designing of*near**optimum*1, W)-HUSBs. ...##
###
Construction of Near-Optimal Vertex Clique Covering for Real-World Networks

2015
*
Computing and informatics
*

are optimal, while the rest of them are

dblp:journals/cai/Chalupa15
fatcat:5ibwflpsdrh2lazgwlmzt6xgxa
*near*-optimal. ... We also present results*for*synthetic pseudorandom*graphs*structured according to the Erdős-Rényi model and Leighton's model. ... Acknowledgement The author would like to thank Jiří Pospíchal and the anonymous referees*for*their very helpful comments on this work. ...##
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Approximating Maximum Weighted Independent Set Using Vertex Support

2009
*
Zenodo
*

Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature

doi:10.5281/zenodo.1078659
fatcat:letlh2m3lrf6bmlz25apzgmxzm
*for*solving the MWIS. ... This paper presents a novel approach to approximate the MWIS of a*graph*using minimum weighted vertex cover of the*graph*. ... to get a*near*smallest weighted vertex cover of the*graph*. ...##
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Multicast tree generation in networks with asymmetric links

1996
*
IEEE/ACM Transactions on Networking
*

*For*

*graphs*

*with*

*bounded*asymmetry, this gives constant times

*optimum*performance guarantee. ... of

*graphs*, and show that the worst-case cost of the tree produced by our algorithm is, at most, twice the

*optimum*cost times the asymmetry,

*for*two of these asymmetry metrics. ... Corollary 4.1: Algorithm SCTF may be used

*for*obtaining trees

*with*

*optimum*average or maximum destination costs as well as obtaining trees

*with*

*near*-

*optimum*(within a factor of two) tree costs. establishing ...

##
###
General models and a reduction design technique for FPGA switch box designs

2003
*
IEEE transactions on computers
*

*For*illustration, we provide

*optimum*hyper-

*universal*ð2; WÞ and ð3; WÞ-switch boxes and a hyper-

*universal*ð4; WÞ-switch box

*with*switch number quite close to the lower

*bound*6W , which is used in a well-known ... Applying this technique, we can design hyper-

*universal*ðk; W Þ-switch boxes

*with*low OðW Þ switches

*for*any fixed k. ... A

*NEAR*

*OPTIMUM*ð4; W Þ-HUSB In this section, we first give a short proof

*for*a lower

*bound*of eðk; W Þ and then present classes of elementary designs

*for*ð4; WÞ-HUSBs

*with*W ¼ 1; . . . ; 7. ...

##
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Scheduling algorithms for multihop radio networks

1993
*
IEEE/ACM Transactions on Networking
*

Previous algorithms could guarantee only that the schedules were

doi:10.1109/90.222924
fatcat:iicgyujtczbehgrjhzhfrqypqe
*bounded*by a length no worse than the maximum node*degree*times*optimum*. ... the network thickness times the*optimum*. ... Previous algorithms could guarantee only that the schedules were*bounded*by a length no worse than the maximum node*degree*times*optimum*. ...##
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Scheduling algorithms for multi-hop radio networks

1992
*
Conference proceedings on Communications architectures & protocols - SIGCOMM '92
*

Previous algorithms could guarantee only that the schedules were

doi:10.1145/144179.144283
dblp:conf/sigcomm/RamanathanL92
fatcat:gcld74q4urajrfewsogbdthnay
*bounded*by a length no worse than the maximum node*degree*times*optimum*. ... the network thickness times the*optimum*. ... Previous algorithms could guarantee only that the schedules were*bounded*by a length no worse than the maximum node*degree*times*optimum*. ...##
###
Scheduling algorithms for multi-hop radio networks

1992
*
Computer communication review
*

Previous algorithms could guarantee only that the schedules were

doi:10.1145/144191.144283
fatcat:5rb6ilo6brfu3ige654tqhl73e
*bounded*by a length no worse than the maximum node*degree*times*optimum*. ... the network thickness times the*optimum*. ... Previous algorithms could guarantee only that the schedules were*bounded*by a length no worse than the maximum node*degree*times*optimum*. ...##
###
Near-Optimal Induced Universal Graphs for Bounded Degree Graphs
[article]

2016
*
arXiv
*
pre-print

n^k ) vertices

arXiv:1607.04911v2
fatcat:o4pfu5umi5hzpcjm2xu7bswla4
*for*the family of*graphs**with*n vertices of maximum*degree*D.*For*constant D, Butler gives a lower*bound*of Ω(n^D/2). ... As a part of the above, proving a conjecture by Esperet et al., we construct an induced*universal**graph**with*2n-1 vertices*for*the family of*graphs**with*max*degree*2. ... Part of our solution*for*the above results is to construct an induced*universal**graph**with*2n−1 vertices*for*the family of*graphs**with*maximum*degree*2. ...##
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Polynomial time approximation schemes for dense instances of NP-hard problems

1995
*
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
*

By dense

doi:10.1145/225058.225140
dblp:conf/stoc/AroraKK95
fatcat:c3kolvccwbee7lzlxc457jizmy
*graphs*we mean*graphs**with*minimum*degree*Ω(n), although our algorithms solve most of these problems so long as the average*degree*is Ω(n). ... The definition of denseness depends on the problem;*for*example, dense*graphs*are*graphs**with*Ω(n 2 ) edges while dense 3-SAT formulas are those*with*Ω(n 3 ) clauses. ... We will show that*with*high probability (over the choice of S) the special partition leads the algorithm to a*near*-*optimum**graph*bisection. ...##
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The fixed angle conjecture for QAOA on regular MaxCut graphs
[article]

2021
*
arXiv
*
pre-print

These fixed angles serve

arXiv:2107.00677v2
fatcat:u73tn32sjnba7lu2haruvfmerq
*for*an optimization-free version of QAOA, and have*universally*good performance on any 3 regular*graph*. ... Heuristic evidence is presented*for*the fixed angle conjecture on*graph*ensembles, which suggests that these fixed angles are "close" to global*optimum*. ... This conjecture has the interesting implication that,*for*regular*graphs*of fixed*degree*and constant edge weight, there is a set of angles that are "*universally*good"*for*any*graph*, in that they may not ...
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